Geodesic
Chvátal's Condition cannot hold for both a graph and its complement
Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 1, pp. 73-76

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Chvátal's Condition is a sufficient condition for a spanning cycle in an n-vertex graph. The condition is that when the vertex degrees are d₁, ...,dₙ in nondecreasing order, i n/2 implies that d_i > i or d_n-i ≥ n-i. We prove that this condition cannot hold in both a graph and its complement, and we raise the problem of finding its asymptotic probability in the random graph with edge probability 1/2.
Keywords: Hamiltonian cycle, Chvátal's Condition, random graph 
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Kostochka, Alexandr; West, Douglas. Chvátal's Condition cannot hold for both a graph and its complement. Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 1, pp. 73-76. http://geodesic.mathdoc.fr/item/DMGT_2006_26_1_a6/